U.S. patent application number 13/687750 was filed with the patent office on 2014-05-29 for reduced cogging torque permanent magnet machine.
This patent application is currently assigned to PRATT & WHITNEY CANADA CORP.. The applicant listed for this patent is PRATT & WHITNEY CANADA CORP.. Invention is credited to Kevin Allan DOOLEY.
Application Number | 20140145525 13/687750 |
Document ID | / |
Family ID | 50772601 |
Filed Date | 2014-05-29 |
United States Patent
Application |
20140145525 |
Kind Code |
A1 |
DOOLEY; Kevin Allan |
May 29, 2014 |
REDUCED COGGING TORQUE PERMANENT MAGNET MACHINE
Abstract
An electric machine is formed by a stator and a rotor that is
free to rotate about an axis of rotation. The stator may have teeth
projecting from a body portion and that define slots for housing
electrical windings. The rotor may have a rotor core and a number
of magnets supported on a peripheral face of the rotor in
substantially contiguous arrangement and of alternating
magnetization. The rotor magnets are shaped so that pairs of
adjacent magnets oppose one another along magnetic boundary lines
that are skewed relative to the slots formed in the body portion of
the stator. For example, the shape of the rotor magnets may be
arcuate trapezoidal or parallelogramatic. In this configuration,
cogging torque experienced by the rotor during operation of the
electric machine may be reduced.
Inventors: |
DOOLEY; Kevin Allan;
(Toronto, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
PRATT & WHITNEY CANADA CORP. |
Longueuil |
|
CA |
|
|
Assignee: |
PRATT & WHITNEY CANADA
CORP.
Longueuil
CA
|
Family ID: |
50772601 |
Appl. No.: |
13/687750 |
Filed: |
November 28, 2012 |
Current U.S.
Class: |
310/51 |
Current CPC
Class: |
H02K 29/03 20130101;
H02K 1/278 20130101; H02K 2201/06 20130101; H02K 1/2706 20130101;
H02K 1/2786 20130101 |
Class at
Publication: |
310/51 |
International
Class: |
H02K 1/27 20060101
H02K001/27 |
Claims
1. An electric machine comprising: a stator comprising a body
portion and a plurality of teeth projecting out of the body
portion, the plurality of teeth being spaced apart angularly from
one another around an axis of rotation and defining a corresponding
plurality of slots in the body portion that are adapted to receive
one or more electrical windings; and a rotor accommodated by the
stator in mutual alignment with and rotatable about the axis of
rotation, the rotor comprising a rotor core and a plurality of
magnets supported on a peripheral face of the rotor core
proximately opposed to the plurality of teeth of the stator across
an air gap, the plurality of magnets arranged to be substantially
contiguous with one another and of alternating magnetization around
the peripheral wall, and each pair of adjacent magnets opposed to
one another along a corresponding magnetic boundary line that is
skewed in relation to each slot formed in the body portion of the
stator.
2. The electric machine of claim 1, wherein each of the plurality
of slots comprises a longitudinal slot opening oriented generally
parallel to the axis of rotation.
3. The electric machine of claim 2, wherein each corresponding
magnetic boundary line is oriented non-parallel to the axis of
rotation.
4. The electric machine of claim 2, wherein the skew of each
corresponding magnetic boundary line has an angular component that
equal to or greater than a corresponding arc length of each
longitudinal slot opening.
5. The electric machine of claim 4, wherein the skew of each
corresponding magnetic boundary line is approximately equal to the
corresponding arc length between each longitudinal slot
opening.
6. The electric machine of claim 1, wherein at least one of the
plurality of magnets has an arcuate trapezoidal shape defined by
non-parallel sidewalls extending between angularly aligned top and
bottom endwalls of different lengths.
7. The electric machine of claim 1, wherein at least one of the
plurality of magnets has an arcuate parallelogramatic shape defined
by parallel sidewalls extending between angularly displaced top and
bottom sidewalls of equal length.
8. The electric machine of claim 1, wherein the plurality of teeth
and the plurality of magnets are each uniformly spaced around the
axis of rotation.
9. The electric machine of claim 8, wherein the number of teeth in
the plurality of teeth is an integer multiple of the number of
magnets in the plurality of magnets.
Description
TECHNICAL FIELD
[0001] The disclosure relates generally to permanent magnet
machines, and more particularly to magnet assemblies for permanent
magnet machines.
BACKGROUND
[0002] Brushless electric machines (including
electronically-commutated and permanent-magnet motors and
generators) have a wide variety of uses and/or applications, for
example, including in electric starters, electrical transport drive
motors, alternators, throttle controls, power steering, fuel pumps,
heater and air conditioner blowers, and engine cooling fans, among
other potential uses and/or applications.
[0003] In a typical brushless machine, a rotor is equipped with a
number of permanent magnets, while the stator houses a number of
electric windings that operate as controlled electromagnets.
Brushless machines can operate in the same way as or similar to
brushed machines, except that for example the mechanical switching
function provided by the combination brush and commutator in a
brushed machine can be replaced by electronic switching of the
windings in a brushless machine. Accordingly, in a typical
brushless motor, permanent magnets mounted to the rotor provide a
static magnetic field relative to the rotor, and a rotating
magnetic field is generated by commutating the stator windings with
electronic switches. Field-Effect Transistors (FETs) and other
types of solid state devices may be used for this purpose.
[0004] For sustained torque generation, a feedback sensor, such as
a Hall effect sensor, can be installed on the stator or
non-rotating structure to detect the angular position of the rotor
in order to control timing of switches.
[0005] Relative to brushed machines, brushless machines have many
potentially significant advantages, including high reliability and
long life. For example, in a brushless motor, bearings are usually
the only parts to exhibit wear over time. Brushless motors also
often outperform brushed motors in applications where high speeds
are required (e.g., above 12,000 RPM) because high speed operation
of brushed motors tends to accelerate wearing of the mechanical
brushes. At the same time, it is also often possible for brushless
motors to achieve more precise and sophisticated motor control
because of their electronic commutation.
[0006] Challenges sometimes associated with brushless machines
include cogging torque, which may be characterized by a non-uniform
torque developed on the rotor as a function of rotor position. Such
torque can be caused by interaction of the rotor magnetization and
angular variations in the magnetic permeance (or reluctance)
between rotor and stator resulting from the geometry of the stator.
Cogging torque may decrease operational efficiency of brushless
motors, and can cause both torsional and radial vibration with
attendant durability and noise problems.
SUMMARY
[0007] In one aspect, the disclosure provides electric machines
having at least one stator and at least one rotor accommodated by
the stator in mutual alignment with, and rotatable about, an axis
of rotation. In various embodiments, machines according to such
aspect of the disclosure include one or more body portions and a
plurality of teeth projecting from the body portion(s), the teeth
being spaced apart angularly from one another around the axis of
rotation and defining a corresponding plurality of slots in the
body portion(s) set parallel to the axis of rotation that are
adapted to receive one or more electrical windings. The at least
one rotor may include a rotor core and a plurality of magnets
supported on a peripheral face of the rotor core proximately
opposed to the plurality of teeth of the stator across a gap, which
may include an air gap. The plurality of magnets may be arranged
such that the magnets are substantially contiguous with one another
and of alternating magnetic orientation around the peripheral wall,
and with each pair of adjacent magnets opposed to one another along
a corresponding magnetic boundary line that is skewed in relation
to each slot formed in the body portion(s) of the stator.
[0008] With such arrangements, cogging torque experienced during
operation of an electric machine may be reduced.
[0009] In some embodiments, one or more of the plurality of slots
may include a longitudinal slot opening oriented generally parallel
to the axis of rotation.
[0010] In some embodiments, one or more corresponding magnetic
boundary lines may be oriented non-parallel to the axis of
rotation.
[0011] In some embodiments, the skew of one or more corresponding
magnetic boundary lines has an angular component that equal to or
greater than a corresponding arc length of each longitudinal slot
opening.
[0012] In some embodiments, the skew of one or more corresponding
magnetic boundary lines is approximately equal to the corresponding
arc length between each longitudinal slot opening.
[0013] In some embodiments, one or more of the plurality of magnets
has an arcuate trapezoidal shape defined by non-parallel sidewalls
extending between angularly aligned top and bottom endwalls of
different lengths.
[0014] In some embodiments, one or more of the plurality of magnets
has an arcuate parallelogramatic shape defined by parallel
sidewalls extending between angularly displaced top and bottom
sidewalls of equal length.
[0015] In some embodiments, the plurality of teeth and the
plurality of magnets may each be uniformly spaced around the axis
of rotation.
[0016] In some embodiments, wherein the number of teeth in the
plurality of teeth may be an integer multiple of the number of
magnets in the plurality of magnets.
[0017] Further details of these and other aspects of the described
embodiments will be apparent from the detailed description
below.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] Reference is now made to the accompanying drawings, in
which:
[0019] FIG. 1 shows a radial cross-sectional view of a turbo-fan
gas turbine engine;
[0020] FIG. 2A shows an exploded perspective view of a permanent
magnet machine having an inner rotor configuration;
[0021] FIG. 2B shows an axial cross-sectional view of a permanent
magnet machine having an inner rotor configuration;
[0022] FIG. 3A shows an exploded perspective view of a permanent
magnet machine having an outer rotor configuration;
[0023] FIG. 3B shows an axial cross-sectional view of a permanent
magnet machine having an outer rotor configuration;
[0024] FIG. 4A shows a perspective view of a rotor magnet
configuration suitable for use in a permanent magnet machine;
[0025] FIG. 4B shows a side view of a rotor magnet configuration
suitable for use in a permanent magnet machine;
[0026] FIG. 4C shows a top view of a rotor magnet configuration
suitable for use in a permanent magnet machine;
[0027] FIG. 5 shows a flattened radial projection of a stator front
face overlaid with rotor magnets of the configuration shown in
FIGS. 4A-4C;
[0028] FIG. 6A shows a perspective view of another rotor magnet
configuration suitable for use in a permanent magnet machine;
[0029] FIG. 6B shows a side view of another rotor magnet
configuration suitable for use in a permanent magnet machine;
[0030] FIG. 6C shows a top view of another rotor magnet
configuration suitable for use in a permanent magnet machine;
and
[0031] FIG. 7 shows a flattened radial projection of a stator front
face overlaid with rotor magnets of the configuration shown in
FIGS. 6A-6C.
DETAILED DESCRIPTION OF EMBODIMENTS
[0032] To provide a thorough understanding, various aspects and
embodiments of machines according to the disclosure, including at
least one preferred embodiment, are described with reference to the
drawings.
[0033] Reference is initially made to FIG. 1, which illustrates a
gas turbine engine 10 of a type preferably provided for use in
subsonic flight, generally comprising in serial flow communication
a fan 12 through which ambient air is propelled, a multistage
compressor 14 for pressurizing the air, a combustor 16 in which the
compressed air is mixed with fuel and ignited for generating an
annular stream of hot combustion gases, and a turbine section 18
for extracting energy from the combustion gases.
[0034] Referring now to FIGS. 2A and 2B, there is generally shown a
permanent magnet (PM) machine 100 suitable for uses or applications
such as a motor, generator, or motor-generator within a gas turbine
engine 10 such as is illustrated in FIG. 1. However, PM machine 100
is not necessarily limited to use only in the gas turbine engine 10
and may be suitable for many other uses or applications, either
with or without modification in the context of the present
disclosure. The PM machine 100 is illustrated in both exploded
perspective (FIG. 2A) and axial cross-sectional (FIG. 2B) views for
convenience.
[0035] In the embodiment shown, PM machine 100 includes a rotor
assembly 110 and a stator assembly 120 supported in mutual
alignment for rotation about an axis of rotation 105. A stator
assembly 120 may be fixedly secured or mounted within the PM
machine 100, for example, on a frame, chassis or other suitable
support member (not shown), while rotor assembly(ies) 110 may be
supported by one or more bearings or other coupling members (not
shown) so as to be rotatable, in relation to the stator assembly
120, and free to spin about the axis of rotation 105 during
operation of the PM machine 100.
[0036] A rotor assembly 110 may include a rotor core 111, which may
for example be supported on rotor shaft 112 and have a generally
cylindrical body shape comprising an outer peripheral face 113 and
opposing end walls 114. As shown in FIGS. 2A and 2B, opposing end
walls 114 may be circular and give the rotor core 111 a generally
circular cross-sectional profile. In other embodiments, rotor core
111 may instead have a polygonal cross-sectional profile, for
example, a hexagon, octagon, or other shape. When used in the
context of the rotor core 111, terms such as "cylindrical" or
"cylindrical shape" may encompass any three-dimensional body having
either a circular or polygonal cross-sectional profile.
[0037] In the embodiment shown, permanent magnets 115 are mounted
on outer peripheral face 111 of rotor core 111, and affixed or
otherwise permanently or removably attached thereto using any
suitable mechanism. For example, permanent magnets 115 may be
affixed to the outer peripheral face 113 using one or more
retaining rings (not shown) or, additionally or alternatively,
using any suitable bonding, laminate or adhesive layer(s), and/or
mechanical fasteners such as rivets, bolts or composite material.
Permanent magnets 115 may be arranged so as to form a contiguous or
pseudo-contiguous ring around outer peripheral face 113, so that
adjacent pairs of magnets 115 oppose one another at magnetic
boundary lines 116 between pairs of magnets 115, either in abutment
or separated by an air gap, depending on how tightly together the
magnets 115 are packed.
[0038] Alternatively, depending on the selection of a suitable
magnetic material, it may also be possible to provide a continuous
layer of magnetic material, as opposed to a plurality of separate
permanent magnets 115. Such continuous magnetic material may be
magnetized in a way that substantially mimics or reproduces the
magnetic field lines generated by permanent magnets 115. For
example, a continuous magnetic material suitable for use in the
described embodiments may be selectively magnetized in
circumferential zones according to a desired magnetic pattern
having skewed magnetic boundaries as are produced by the
arrangement of permanent magnets 115 as described herein. Suitable
magnetic materials for a continuous magnetic material may include
alloys of neodymium, such as neodymium-iron-boron (NdFeB) alloys,
or alternatively alloys of samarium-cobalt (SmCo), among others
potentially. However, separately manufactured and bonded magnets
such as permanent magnets 115 may in at least some cases provide a
more cost effective implementation than a continuous magnetic
layer.
[0039] Permanent magnets 115 may be arranged to have alternating
(North-South-North) magnetization in generally radial directions
around outer peripheral face 113. With such arrangements, every
second one of permanent magnets 115 may be aligned based on
geometry and pointed in the same axial direction (e.g., with
reference to the small end of the permanent magnets 115) and each
having magnetizations characterized by "North" poles. Every other
second one of permanent magnets 115 may thereby by aligned by
geometry and pointed in the same but opposite axial direction
(e.g., again with reference to the small end of the permanent
magnets 115) and each having magnetizations characterized by
"South" poles. In this arrangement, which is indicated in FIGS. 2A
and 2B, half of permanent magnets 115 have a given magnetization
which is opposite to the magnetization of another half of permanent
magnets 115. Thus, magnetic flux may either emanate out of and lead
into the outer peripheral face 113 in a generally radial direction,
respectively, depending on the given magnetization of each
permanent magnet 115. For convenience, such arrangement of
permanent magnets 115 is referred to as having an "alternating
magnetization". Further description of permanent magnets 115 is
provided below with particular reference to FIGS. 4A-4C and
6A-6C.
[0040] In the embodiment shown, stator assembly 120 includes a
stator body portion 121 that defines an interior space shaped and
sized to accommodate rotor assembly 110 within the interior space.
(Such a configuration is commonly referred to as an "inner rotor"
or "inside rotor" configuration to reflect the relative positioning
of the rotor assembly 110 within the interior space). As shown in
FIGS. 2A and 2B, stator body portion 121 may be annular or
ring-shaped, for example, with the effect of conserving material,
but in general may be any other three-dimensional body defining a
suitably sized interior space for accommodating the rotor assembly
110 therewithin.
[0041] More particularly, an interior space compatible with the
disclosure may have a cross-sectional profile matched to a uniform
or varying cross-sectional profile of the rotor assembly 110
(including both the rotor core 111 and the magnets 115), but of a
slightly larger size, so as to provide a small air gap 122 between
the magnets 115 and the stator body portion 121. The air gap may
have a generally constant radial width of a pre-determined value to
improve the operation of the PM machine 100, as explained further
below.
[0042] A number of teeth 123 may be formed or otherwise provided in
the stator body portion 121 and which define a corresponding number
of slots 124 interleaved between the teeth 123. Some or all of
teeth 123 may have a stem portion 125 projecting from the stator
body portion 121 in an inwardly radial direction, and which may
flare into two tangential arm portions 126. Accordingly, each slot
124 may be formed to include a slot opening 127 between an opposing
pair of tangential arm portions 126, one from each of a
corresponding adjacent pair of the teeth 123. In various
embodiments, slot opening(s) 127 may have longitudinal shape(s),
profile(s), or trajectory(ies) oriented generally parallel to axis
of rotation 105.
[0043] Further, some or all of slots 124 may gradually expand, in
an outwardly radial direction, into relatively larger cavity
portion(s) in which electrical windings 128 may be wound. For
convenience, electrical windings 128 are depicted as disconnected
circuit paths (e.g., wires), although electrical windings 128 may
include any number of continuous paths. Electrical windings 128 be
connected to an external drive circuit (not shown) that includes at
least one electronic switch, such as a FET or other switchable
semiconductor device that may provide electronic commutation of
electrical windings 128 during operation of the PM machine 100.
[0044] Tangential arm portions 126 may be sized such that inner
faces of teeth 123 form an inner peripheral face 129 of the stator
body portion 121, which is continuous except where broken by slot
openings 127. Inner peripheral face 129 may be proximately opposed
to outer faces of magnets 115 across the air gap 122 to promote
electromagnetic interaction between the static magnetic field
generated by the magnets 115 and the rotating magnetic field
generated by commutation of the electrical windings 128.
[0045] The size and shape of slot openings 127 may be a compromise
between manufacturing cost and electromagnetic properties of PM
machine 100. For example, slot openings 127 having a larger width
may tend to reduce manufacturing cost by simplifying threading of
the electrical windings 128 into the slots 124, whereas a smaller
width for the slot openings 127 may tend to provided improved
electromagnetic properties by reducing angular variations in the
magnetic permeance of the air gap 122.
[0046] In some cases, the size of slot openings 127 may also be
selected so as to effect control over a short circuit current
generated within a permanent magnet machine. As the size of slot
opening 127 may tend to affect the inductance of the electrical
winding 128 housed therewithin, short circuit current flowing in
the electrical winding 128 may be limited through control over
inductance (which in turn may be related to the size of slot
opening 127. Further description of the relationship(s) between
slot openings 127, inductance of electrical windings 128, and short
circuit current may be found in U.S. Pat. No. 7,119,467, filed Mar.
21, 2003, and entitled "CURRENT LIMITING MEANS FOR A GENERATOR",
the entirety of which is herein incorporated by reference.
[0047] Referring now to FIGS. 3A and 3B, there is generally shown a
permanent magnet (PM) machine 200 in both exploded perspective
(FIG. 3A) and axial cross-sectional (FIG. 3B) views. In certain
respects, the configuration and operation of PM machine 200 may be
similar to PM machine 100 shown in FIGS. 2A and 2B, except that the
PM machine 200 has an "outer rotor" or "outside rotor"
configuration to reflect a different relative positioning of parts.
For convenience, some description of the PM machine 200 that is
common to the PM machine 100 may be omitted or abbreviated, while
specific differences and/or dissimilarities may be emphasized or
highlighted.
[0048] The PM machine 200 generally may include a rotor assembly
210 and a stator assembly 220, unlike the PM machine 100, now with
the stator assembly 220 shaped and sized so as to be accommodated
within an interior space defined by the rotor assembly 210. The
rotor assembly 210 includes a rotor core 211 that may be a
generally annular or shell-like body having an inner peripheral
face 212 extending between opposing end walls 213. When used in the
context of the rotor core 211, terms such as "annular" or "annular
shape" may encompass any three-dimensional shell-like body having
either a circular or polygonal cross-sectional profile. The rotor
core 211 may be supported rotatably within the PM machine 200 on
one or more bearings or other coupling members (not shown).
[0049] Permanent magnets 215 may be affixed or otherwise secured to
inner peripheral face 212 of rotor core 211 (e.g., using a
retaining ring, bonding or adhesive layer or other suitable
mechanism). Similar to permanent magnets 115 (FIGS. 2A and 2B),
permanent magnets 215 may be arranged around an inner peripheral
face 212 with alternating magnetization (as indicated in FIGS. 3A
and 3B), and forming a contiguous or pseudo-contiguous ring or
shell of magnetized material. Adjacent pairs of magnets 215 may
thereby again oppose one another at corresponding magnetic
boundaries 216 between adjacent pairs of magnets 215, either in
abutment or separated by a small air gap depending on how tightly
together permanent magnets 215 are packed.
[0050] Stator assembly 220 may include a stator body portion 221 in
which are formed a number of teeth 223 that define corresponding
slots 224 in the stator body portion 221. Similar to teeth 123
(FIGS. 2A and 2B), teeth 223 may have a stem portion 225 that
gradually flares into two tangential arm portions 226, with stem
portion 225 projecting out of stator body portion 221 toward
magnets 215 in an outwardly radial direction. Thus, each of slots
224 may be formed to include a slot opening 227 between an opposing
pair of tangential arm portions 226, which may gradually expand in
an inwardly radial direction into a relatively larger cavity
portion in which electrical windings 228 are wound. Electrical
windings 228 may lead to an external drive circuit and, for
convenience, are again depicted as separate windings.
[0051] The size and shape of teeth 223 may again be such that an
outer peripheral face 229 of the stator body portion 221, which is
continuous except where broken by the slot openings 227, opposes
magnets 215 across an air gap 222 of generally uniform radial
thickness. Thus, an interior space defined by the rotor core 211
may have a cross-sectional profile matched to the cross-sectional
profile of the stator assembly 220, but of a slightly larger
radius. As used herein throughout in the context of either rotor
core 111 and stator body 121 (FIGS. 2A and 2B) or rotor core 211
and stator body 212 (FIGS. 3A and 3B), the term "accommodated by"
may encompass any shaping, sizing, spatial arrangement,
disposition, and/or combination thereof, and/or any other
configuration wherein one of rotor and stator may be housed,
tightly or otherwise, within an interior space defined by the other
of the rotor component so as to promote electromagnetic interaction
of the static and rotating magnetic fields generated by these
components.
[0052] In various embodiments, PM machines 100, 200 may operate in
one or more different modes of operation, including at least a
motor mode of operation and a generator mode of operation. During
operation in a motor mode, drive voltage may be applied to
electrical windings 128, 228 by, for example, an external voltage
supply coupled to the electrical windings 128, 228. Thereafter, an
electrical current flowing in the windings 128, 228 may induce a
magnetic flux in the stator body portion 121, 221 having a rotating
field configuration, which interacts with the static magnetic field
generated by permanent magnets 115, 215. By commutating the
externally applied drive voltage, a torque may be developed on the
rotor core 111, 211 causing rotation thereof about the axis of
rotation 105, 205.
[0053] Alternatively, when PM machines 100, 200 are operated in
generator mode (sometimes also referred to as an "alternator
mode"), an external torque may be exerted on the rotor core 111,
211 by, for example, a coupled load. As the rotor core 111, 211
rotates in response to the externally applied torque (or if already
rotating in a counter direction, in resistance to the externally
applied torque), a rotating magnetic field generated by the
permanent magnets 115, 215 interacts with the structure of stator
body portion 121, 221. This interaction produces a magnetic flux
within stator body portion 121, 221 that loops windings 128, 228
and induces a terminal voltage across windings 128, 228. If
windings 128, 228 are closed by an external circuit, the induced
terminal voltage may be used to power one or more electrical loads
driven by the external circuit, charge a storage device, or for any
other suitable purpose.
[0054] In either mode of operation, practical and/or other
non-ideal characteristics of PM machines 100, 200 may result in the
creation of cogging torque during use. For example, owing to
angular variation in the radial thickness of the stator body
portion 121, 211, the magnetic permeance of the air gap 122, 222
may vary at different angular positions around the air gap 122,
222, depending on the presence or absence of magnetic material in
the stator body portion 121, 211. In particular, the absence of
magnetic material at various angular positions (i.e., at the
locations of the slots 124, 224) can reduce the apparent magnetic
permeance of the air gap 122, 222 relative to the permeance at
other angular positions that coincide with the existence of
magnetic material (i.e., at the locations of the stator teeth 123,
223). Simultaneously, a static magnetic field generated by the
permanent magnets 115, 215 may exhibit radial variations due to
leakage flux between pairs of adjacent, oppositely polarized
magnets 115, 215 (i.e., of alternating magnetization. Such leakage
flux can cause the magnetic field created in the vicinity of the
magnetic boundaries 116, 226 to be generally weaker than the
magnetic field existing near the center of the magnets 115, 225. A
similar effect on the apparent permeance of the air gap 122, 222
can also in some cases result from magnetic saturation at one or
more edges of stator teeth 123, 223. Thus, a contribution to
cogging torque can be provided through either or both of these
practical/non-ideal characteristics of a PM machine 100, 200.
[0055] As a rotor core 111, 121 spins about its axis of rotation
105, 205, at one or more discrete angular positions, one or more of
magnetic boundaries 116, 216 between adjacent pairs of magnets 115,
215 may be directly opposed to one of slots 124, 224 rather than
the front faces of the stator teeth 123, 223. When this occurs, a
different magnetic field may be generated at magnetic boundaries
116, 216 and the relatively small apparent magnetic permeance of
the air gap 122, 222 may interact to create an unbalance of
tangential magnetic forces that alters the overall torque developed
on the rotor core 111, 121. (At other angular positions, where no
or less unbalance of tangential magnetic forces exists, the rotor
core 111, 121 experiences a relatively uniform positive and
negative torque, resulting in a net zero torque developed between
the stator and rotor).
[0056] In brushless motors, such as PM machines 100, 200, cogging
torque may serve as a significant, and even primary, source of
vibrations, noise and torque fluctuations. As such, cogging torque
may pose a significant design constraint in brushless motors. For
example, vibrations and noise may affect performance and increase
equipment wear, while torque fluctuations may become a particularly
significant factor in high-performance, control applications, and
in smooth starting/stopping of rotor rotation. Embodiments
according to the disclosure may be suitable to eliminate, or at
least to reduce the effects of, the cogging torque experienced by
the rotor core 111, 211 during use and, thereby, to achieve
improved starting/stopping, as well as more efficient and/or less
destructive operation of PM machines 100, 200.
[0057] When a PM machine 100, 200 is operated in a generating mode,
and cogging torque is reduced, at least in part, by utilizing
configurations of magnets 115, 215, as described herein,
improvement in the characteristics of an induced terminal voltage
waveform may in some cases also be achieved. For example, by
reducing cogging torque, harmonic distortion in an induced terminal
voltage on electrical windings 128, 228 of a PM machine 100, 200
may also be reduced, which can advantageously lead to a more
sinusoidal voltage waveform being developed. As output power in PM
machine 100, 200 may generally correspond to input power
(notwithstanding losses due to practical or non-ideal components),
given a relatively constant speed, a non-steady state input power
(such as might be expected if significant cogging torque or other
torsional disturbance is developed) may be expected to translate
into harmonic distortion in the output power characteristic.
Conversely, to achieve an ideal or near ideal 3-phase sine function
in output power might imply no or very little cogging torque and/or
torsional disturbance being present.
[0058] Referring now to FIGS. 4A-4C, there is shown a configuration
of a rotor magnet 300, which may be suitable for use in either a PM
machine 100 (FIGS. 2A-2B) or a PM machine 200 (FIGS. 3A-3B). In the
embodiment shown, rotor magnet 300 has an arcuate trapezoidal
(sometimes referred to as a "keystone") shape defined by a top end
wall 305, a bottom end wall 310, side walls 315, an inner face 320,
and an outer face 325 generally opposing the curved inner face
420.
[0059] Top end wall 305 may be angularly aligned with and generally
parallel to, but of a different length than, the bottom end wall
310. In some embodiments, top end wall 305 may be shorter than
bottom end wall 310 to provide the rotor magnet 300 with such
generally trapezoidal or keystone configuration. As used herein
throughout in the context of the rotor magnet 300, the terms "top
end wall" and "bottom end wall" do not necessarily indicate or
relate direction, orientation or alignment in an absolute sense.
Rather these terms are used for convenience to reference different
aspects or features of the rotor magnet 300. For example, "top end
wall" and "bottom end wall" may refer merely to the shorter and the
longer of these two end walls, respectively.
[0060] Inner face 320 and outer face 325 of magnet 300 are
generally parallel to one another and each have a curved or arcuate
surface contour defined by a corresponding radius of curvature. As
explained further below, the radius of curvature of inner face 320
may be approximately equal to the radius of curvature of the outer
peripheral face 113 of the rotor core 111 to allow for a tight fit
between rotor magnet 300 and a rotor core 111. Alternatively, in
the case of the PM machine 200, the radius of curvature of outer
face 325 may be approximately equal to the radius of curvature of
the inner peripheral face 212 of the rotor core 211 to provide
tight fit.
[0061] Sidewalls 315 extend between top and bottom end walls 305
and 310 are generally non-parallel to one another on account of the
different lengths of the top and bottom end walls 305 and 310. In
some embodiments, the sidewalls 315 are approximately of equal
length to provide the rotor magnet 300 with an "isosceles"
trapezoidal shape, whereby the angle subtended between each of the
sidewalls 315 with the top end wall 305 (or bottom end wall 310)
are equal or nearly equal. The sidewalls 315 may also be tapered,
sloped or otherwise angled inwardly so that, when installed on the
rotor core 111 (or the rotor core 211), the sidewalls 315 are
oriented essentially orthogonal to the outer peripheral face 113
(or inner peripheral face 213). Thus, when a number of rotor
magnets 300 are installed on either a rotor core 121 or 221,
opposing sidewalls 315 from adjacent magnets may be brought into
abutment or near abutment.
[0062] Referring back to FIGS. 2A-2B, each of a plurality of
magnets 115 may have the configuration of the rotor magnet 300
shown in FIGS. 4A-4C. With such configuration, the plurality of
magnets 115 may be affixed to the outer peripheral wall 113 in
alternating relative orientation and magnetization to create a
continuous or pseudo-continuous surface layer of magnetic material.
Within the present disclosure, the term "alternating relative
orientation" may used in reference to the geometric or spatial (as
opposed to magnetic) configurations of rotor magnets 300, e.g., to
reflect that adjacent rotor magnets 300 may point in opposite axial
directions. However, relative orientation may also be related to
magnetization in some cases. For example, each rotor magnet 300 may
be magnetized so that the top end wall 305 is designated as "North"
and the bottom end wall 310 is correspondingly designated as
"South". Alternating relative orientation thereby also alternates
the relative magnetizations of the plurality of magnets 115,
215.
[0063] So that a plurality of magnets 115, in the case of a PM
machine 100, is shaped into a generally cylindrical surface layer
that fits tightly to and substantially circumscribes the outer
peripheral wall 113 of the rotor core 111, not just radius of
curvature, but also the number and size of the plurality of magnets
115 may be selected appropriately. In some embodiments, each rotor
magnet 300 may have approximately the same arc length, optionally,
selected as an integer fraction of the circumference of the
peripheral face 113. Where each rotor magnet 300 is equally sized,
when installed on the rotor core 111, the plurality of magnets 115
will also be uniformly spaced around the peripheral face 113.
However, it may also be possible in some cases to use rotor magnets
300 of generally different sizes and still achieve tight fit and
circumscription of the outer peripheral wall 113.
[0064] The number of the plurality of magnets 115 is variable and,
optionally, may be related to the number of the teeth 123 formed in
the stator body portion 121. In some cases, for example, such
relationship may be as an integral fraction of the number of number
of teeth 123. Thus, the number of the plurality of magnets 115 may
equal the number of the teeth 123 or, alternatively, may be equal
to one half, one third, one quarter, or any other integral
fraction, of the number of the teeth 123. If related to the number
of teeth 123 formed in the stator body portion 121, the number of
the plurality of magnets 115 will in general be an even number
(because the number of magnets 115 may be an even number of North
and South polarized magnets). Generally, the number of teeth 123
and the number of magnets 115 may be related by the number of
electrical phases to be generated in the PM machine, but could
potentially may be related by some other requirement in alternative
embodiments. In some embodiments, the plurality of teeth 123 may
also be uniformly spaced around the inner peripheral face 129.
[0065] A trapezoidal or keystone shape of the rotor magnet 300 may
also in some cases facilitate tight fitting on the rotor core 111.
Due to machining tolerances and other practical limitations, it is
not always possible or cost effective to manufacture rotor magnets
300 with precise and consistent dimensionality. With other
configurations of rotor magnets, this machine tolerance would
sometimes result in the formation of small air gaps between
adjacent magnets when installed on the rotor face, which tend to
adversely affect rotor balance.
[0066] However, with a trapezoidal configuration of rotor magnets
300, the presence of air gaps may be significantly reduced or
eliminated altogether by allowing for slight axial displacement of
one or more of the magnets 115. Even accounting for machining
tolerances, by axial displacement of any or all of magnets 115
along the rotor core 111, opposing sidewalls 315 from adjacent
pairs of the magnets 115 may be brought into near or substantial
abutment with (in general "opposed to") one another at
corresponding magnetic boundaries 116. Resulting axial displacement
of the magnets 115 tends to have only a relatively minor impact, if
any, on the magnetic properties or performance of the PM machine
100. Accordingly, less accurate machining of the rotor magnet 300
may be possible without adversely affecting fit or rotor
balance.
[0067] While the above description makes explicit reference to
features and aspects of the PM machine 100 to explain various
advantages of the rotor magnet 300, such description may apply
equally to the PM machine 200 shown in FIGS. 3A-3B with appropriate
modification or variation to reflect the "outside rotor"
configuration of the PM machine 200. For example, similar to the PM
machine 100, each of a plurality of magnets 215 in the PM machine
200 may also be realized using the rotor magnet 300 shown in FIGS.
4A-4C, except that the rotor magnets 300 may be affixed or
otherwise secured to the inner peripheral face 212 of the rotor
core 211. Otherwise, additional description of the plurality of
magnets 215 may be found above in respect of the plurality of
magnets 115 and, for convenience, will not be repeated here.
[0068] Referring now to FIG. 5, relative spatial relationships of
rotor magnets 300 and stator slots is explained in further detail.
For convenience, FIG. 5 shows a partial flattened, side projection
of a stator body 121 (FIGS. 2A-2B) overlaid with a number of the
rotor magnets 300. (Slight axial displacement of the rotor magnets
300 may be exaggerated in FIG. 5 to illustrate how tight packing of
adjacent magnets may be achieved).
[0069] As described above, rotor magnets 300 are arranged in
alternating magnetization and axial orientation and so that
adjacent, oppositely magnetized pairs are generally opposed to one
another at corresponding magnetic boundaries 116, 216. The number
of the rotor magnets 300 shown in FIG. 5 is equal to half the
number of stator teeth 123, so that the number of magnetic
boundaries 116, 216 between opposing magnets 300 is also equal to
half the number of stator slots 124, 224 formed between adjacent
pairs of the teeth 123. In some embodiments, the number of teeth
123 may be equal to 12, 18, or some other multiple, such as an even
multiple of three, as the case may be, depending on a number of
poles formed in a PM machine 100, 200.
[0070] While FIG. 5 depicts a configuration of rotor magnets 300
that number half a corresponding number of stator teeth 123, as
noted, other relative numberings are possible. Also, as described
further below, the degree of cogging torque reduction will in
general depend on the relative numbering of rotor magnets 300 to
stator teeth 123. Arrangements such as FIG. 5 illustrates, in which
the number of stator teeth 123 are an integer multiple of the
number of magnets 300, may provide optimized (or at least
pseudo-optimized) cogging torque reduction. The particular
arrangement shown in FIG. 5 is for convenience of illustration
only.
[0071] Each of the magnets 300 may also have substantially the same
dimensions so that the angular spacing of the magnets 300 around
the axis of rotation 105, 205 is uniform (equal to 2.pi./N.sub.m,
where N.sub.m is the number of the rotor magnets 300). The stator
teeth 123 may also have uniform angular spacing around the axis of
rotation 105, 205 (given by 2.pi./P, where P=N.sub.p.times.M and is
equal to the product of the number N.sub.p of poles and the number
M of electrical phase windings). With these numbers and respective
angular spacings of rotor magnets 300 and stator teeth 123, at
certain angular positions of the rotor 111, 211, each of the
magnetic boundaries 116, 216 is generally opposed to a
corresponding one the stator slots 124, 224 across the air gap 122,
222 (FIGS. 2B and 3B).
[0072] Due to the trapezoidal shape and alternating configuration
of the rotor magnets 300, magnetic boundary lines 116, 216 are
skewed in relation to the orientation of slots 124. For example,
slots 124 are oriented in a generally axial direction as defined by
axis of rotation 105, 205, while the magnetic boundary lines have a
non-zero angular component. Consequently, the projection of the
magnetic boundary lines 116, 216 onto the flattened surface of the
stator body intersects, and is not parallel, with the general
trajectory of the slots 124. (Because the slots 124 have some
finite width, the "general trajectory" of the slots is approximated
by the magnetic boundary line running midway between adjacent pairs
of teeth 123, 223.)
[0073] Skewing magnetic boundaries 116, 216 in relation to stator
slots 124 tends to reduce the development of cogging torque during
operation of the PM machine 100. As the rotor 111 spins, angling of
magnetic boundary lines 116, 116 relative to the general trajectory
of the slots 124 tends to reduce the imbalance of tangential
magnetic forces that contribute to the cogging torque. Without
skewing of magnetic boundary lines 116, the coincidence of the
weakened magnetic field associated with the magnetic boundary lines
116 with areas of relatively low magnetic permeance is localized to
a very narrow range of angular positions in which the magnetic
boundary lines 116 project onto the stator slots 124. However, when
magnetic boundary lines 116 are skewed in relation to the stator
slots, the coincidence is spread out onto a larger range of angular
positions to thereby provide more evenly balanced magnetic forces
throughout each rotational cycle of the PM machine 100.
[0074] As shown in FIG. 5, the skew of the magnetic boundary lines
116 (measured in terms of angular component) is approximately equal
to the arc length of the slot opening 124. However, the amount of
skew provided may be varied in different embodiments and may
generally be greater than or equal to the arc length of the slot
opening 124. For example, increasing the amount of skew provided
may tend to reduce or ameliorate adverse effects associated with
cogging torque, but in general will also result in less torque
generation overall. Conversely, less skew will in general increase
overall torque generation, but may also tend to result in greater
exhibition of cogging torque. Accordingly, the amount of skew may
be varied to meet one or more different, and in some cases
competing, design constraints and/or specifications.
[0075] In some embodiments, the angular component of the skew may
depend on the radial width of the air gap to achieve a
design-optimized reduction of cogging torque. Alternatively, or
additionally, the angular component of the skew may depend on the
distance between centers of teeth 123, 223 or between slot openings
124, 224, for example, as determined by the angle between each of
the teeth 123, 223 or the angular width of opposing tangential arm
portions 126 in stem portion 125. The angular component of the skew
may further depend on the axial length or height of the stator body
portion 121, 221.
[0076] An optimal (or pseudo-optimal) reduction of cogging torque
may in some cases be achieved when magnets 300 are arranged
relative to stator teeth 123, 223 such that one end of a given
magnet 300 will be at a given position relative to a tooth 123,
223, and the opposite end of that magnet 300 will be at the same
relative position on an adjacent tooth 123, 223. In some cases, a
trapezoidal shaped magnet 300 may be half a tooth wider at one end
and half a tooth narrower at the opposite end of magnet 300,
thereby providing for a total difference of one tooth width taken
from one end of magnet 300 to the opposite end.
[0077] The relationship designed to provide optimal (or
pseudo-optimal) reduction of cogging torque may be expressed
mathematically as follows:
.phi. m = tan - 1 ( 2 .pi. N R s L s ) , ( 1 ) ##EQU00001##
where .phi..sub.m may represent a magnetic boundary edge angle
relative to a tooth mean centre line for minimum cogging torque.
For trapezoidal (keystone) shaped magnets 300, .phi..sub.m may be
the angle of one side edge of magnet 300 relative to the opposite
side edge (see FIGS. 4A-4C).
[0078] In equation (1) above, R.sub.s represents a radius of stator
body portion 121, 221 (or tooth surface), N represents a number of
slots 124, 224 defined in stator body portion 121, 221, and L.sub.s
represents the axial length of a tooth 123, 223 swept by the magnet
(included or common surface between magnet and tooth). Based on
these defined parameters, magnet edge angle relative to the axis of
tooth mean centerline is computed as the inverse tangent defined by
equation (1), i.e., of the quotient of 2.pi. multiplied by tooth
surface radial position (stack diameter divided by two) and divided
by the product of magnet included stack length and the number of
slots 124, 224. As used herein, the term "magnet included stack
length" may denote either the hypothetical axial length of the
magnet if the stack was longer than the magnet or, alternatively,
the hypothetical axial length of the stack if the magnet was
axially longer than the stack.
[0079] The corresponding reduction in output torque when a PM
machine is operating in motor mode from skewing of magnets as
described herein may be given as follows:
T c = T n cos ( .pi. 2 N m N ) , ( 2 ) ##EQU00002##
where T.sub.c represented corrected torque, T.sub.n represents
nominal torque, N.sub.m represents a number of magnets (or poles),
and N represents a number of slots (or teeth). Similarly, where a
PM machine is being operated in a mode generator, the corresponding
reduction in output voltage due to skewing of magnets may be given
as follows:
V c = V n cos ( .pi. 2 N m N ) , ( 3 ) ##EQU00003##
where V.sub.c represents corrected Voltage, V.sub.n represents
nominal Voltage, and N.sub.m and N are defined as above for
equation (2).
[0080] Based on the above equation, it is also possible to
configure magnets 300 to provide a reduction in cogging torque
ranging any amount generally from zero (no reduction) to the
optimal (or pseudo-optimal) reduction indicated above. At maximum
reduction in cogging torque, there may be experienced a reduction
in available torque and voltage generation by about 15% from
optimum settings. Accordingly, in some embodiments, there may exist
a trade off between reduced cogging torque, output waveform
distortion, and output power at a given size and speed of a
machine.
[0081] Referring now to FIGS. 6A-6C, there is shown a configuration
of a rotor magnet 400, which may be suitable for use in either PM
machine 100 (FIGS. 2A-2B) or PM machine 200 (FIGS. 3A-3B). Rotor
magnet 400 is shaped into an arcuate parallelogram defined by
opposing end walls 405 and 410, opposing sidewalls 415, inner face
420, and an outer face 425 generally opposing the curved inner face
420. In some embodiments, rotor magnet 400 may be used as
alternative to, or simultaneously with, the rotor magnet 300 (FIGS.
4A-4C).
[0082] End walls 405 and 410 may be generally parallel to one
another and of the same length, but angularly displaced relative to
a central axis (not shown) of the rotor magnet (400). Sidewalls 415
extend between the end walls 405 and 410 are also generally
parallel to one another on account of the equal lengths of the end
walls 405 and 410. Sidewalls 415 may also be tapered, sloped or
otherwise angled inwardly so that, when installed on the rotor core
111 (or the rotor core 211), sidewalls 415 are oriented essentially
orthogonal to the outer peripheral face 113 (or inner peripheral
face 213). Similar to the above description, such angling of
sidewalls 415 may facilitate arrangement of a number of the rotor
magnets 400 with near or substantial abutment. For this purpose,
the shape of the magnet 400 may also allow for slight axial
displacement to ensure tight fit.
[0083] Similar to inner face 320 and outer face 325, inner face 420
and outer face 425 are generally parallel and each have a curved or
arcuate surface contour defined by a corresponding radius of
curvature that is approximately equal to the radius of curvature of
the outer peripheral face 113 or the inner peripheral face 213,
respectively. Again, this shaping of the rotor magnet 400 may
facilitate fitting of a number of the magnets 400 tightly to the
rotor core 111 or 121.
[0084] Referring now to FIG. 7, exemplary relative spatial
relationships of rotor magnets 400 and stator slots are explained
in further detail. Again, for convenience, FIG. 7 shows a partial
flattened, side projection of the stator body 121 shown in FIGS. 2A
and 2B overlaid with a number of the rotor magnets 400.
[0085] In the embodiment shown in FIG. 7, rotor magnets 400 are
arranged in alternating orientation and magnetization around axis
of rotation 105, 205 so that adjacent pairs are generally opposed
to one another at corresponding magnetic boundaries 116, 216.
Similar to the arrangement of FIG. 5, the number of the rotor
magnets 400 shown in FIG. 7 is equal to half (although it need not
be) the number of stator teeth 123, 223, so that the number of
magnetic boundaries 116, 216 between opposing magnets 400 is also
equal to half the number of stator slots 124, 224 formed between
adjacent pairs of the teeth 123, 223. However, in alternative
embodiments, the number of teeth 123, 223 may be other integer
multiples of the number of magnets 400.
[0086] Due to the slanted rectangular shape and alternating
configuration of the rotor magnets 400, the magnetic boundary lines
116, 216 are also skewed in relation to the orientation of the
slots 124, 224. Consequently, the projection of the magnetic
boundary lines 116, 216 onto the flattened surface of the stator
body again intersects, and is not parallel, with the general
trajectory of the slots 124, 224, which, like the skewing achieved
by the rotor magnet 300, tends to reduce the development of cogging
torque during operation of a PM machine 100, 200.
[0087] Similar to trapezoidal magnets 300 (FIGS. 4A-4C), different
spatial relationships of parallogrammatic rotor magnets 400 and
stator slots as shown in FIG. 7 may realize different relative
reductions of cogging torque. In some embodiments, the relationship
expressed in equation (1) above may again yield optimal (or
pseudo-optimal) cogging torque reduction, where .phi..sub.m for
parallelogram shaped magnets 400 may be the angle of each parallel
side edge of magnet 400 relative to the slot edge (see FIGS.
6A-6C). In such cases, the expressions defined in equations (2) and
(3) for corresponding reduction in output torque or voltage
resulting from skewing of magnets as described herein may again
hold true.
[0088] The above description is meant to be exemplary only, and one
skilled in the art will recognize that changes may be made to the
embodiments described without departing from the scope of the
invention disclosed. For example, the relative number and sizing of
rotor magnets may be varied in relation to the number of slots
defined in the stator. Additionally, the rotor magnets need not all
have the same shape or configuration and at least some of the rotor
magnets may have a different configuration. In some cases, each
magnetic boundary between adjacent rotor magnets may be skewed in
relation to the stator slots, although in other cases, one or more
of the magnetic boundaries may not be. Still other modifications
which fall within the scope of the present invention will be
apparent to those skilled in the art, in light of a review of this
disclosure, and such modifications are intended to fall within the
appended claims.
* * * * *